Which of the following represnt the range of the function y=-1/2(x+10)^2+14?
1) y> =-5 2)y> =10 3) y< =7 4) y< =14, explain plz

The answer is option is (4) y ≤ 14

Step-by-step explanation:

The given function, y = - 0.5

We have to find the range of this function. If we take the first part of the function alone we can see that it is always negative or zero. So the maximum value of the function is 14.

This happens when we make the first part zero and for that we put x = -10.

So the maximum value of the function occurs at x = -10 and that value is y = 14.

Hence the range is y ≤ 14.

The answer is option is (4) y ≤ 14

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.